How to get those multicolored shadows?
Those are not colored shadows, shadows don't have a color per-se, they are just e slightly colored light sources.

Just add a slight tint to your lamp objects so one has a warmer redish tone, and the other has a cooler tone towards blueish or green.

This is generally done using a Three Point Light system, which is a well know lighting technique in photography also.



Optionally if you want more realistic shadows or natural lighting use a sphericall environment map in your scene's World nodes, Ideally HDR based or as regular JPG image.